Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C5×D5×D31⋊C3 |
| unambiguous semidirect product | (C5×D5×D31)⋊C32 |
| unambiguous semidirect product | (C3×C5×D5×D31)⋊C3 |
| Fitting, socle | C3×C52×C31 ⋊ C22×C3 |
| derived | C5×C31 ⋊ C22×C32×C5 |
| Hall | C3×C52×C31⋊C3 ⋊ C22 |
| Hall | C5×D5×D31 ⋊ C32 |
| Hall | C52×C31 ⋊ C22×C32 |
| Hall | C3×C31⋊C3 ⋊ C2×C5×D5 |
| Sylow | C31 ⋊ C2×C32×C5×D5 |
| Sylow | C52 ⋊ C2×C3×D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D5×D31⋊C3 |
| commutator, cosocle, hypocenter | C5×C31 | C22×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C31 | C22×C3 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C3×C5 | |
288 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 500);